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When is a proof? (2581 words) |
 | Not believing their result, the two decided to look again at Goldston and Yildirim's core lemmas to see if there was some crucial detail that was being too easily glossed over. |
| It wasn't that the established procedure was in itself wrong; rather, it did not apply under the new circumstances in which Goldston and Yildirim were using it. |
| Goldston and Yildirim's core lemmas had a familiar flavor and their conclusions were very believable, so everyone believed them. |
| American Institute of Mathematics (454 words) |
| Number theorists moved a step closer to the resolving the twin prime conjecture this week when a new paper appeared on the internet, see the AIM preprint, which gives a proof that the spacing between consecutive primes is sometimes very much smaller than the average spacing. |
| This result was originally reported two years ago by Dan Goldston and Cem Yildirim (see the original AIM press release and technical description) but was later retracted. |
| Dan Goldston and Cem Yildirim have smashed all previous records on the size of small gaps between prime numbers. |
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